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REVIEW 4 major objections 4 minor 62 references

Broadband Control of Light through Complex Media via Automatic Self-Referencing Transmission Matrix Characterisation

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Pith's one-line read The paper claims that the full complex transmission matrix of a multimode fibre can be recovered from camera intensity frames alone, by using every propagating mode as a distributed phase reference rather than relying on an external or pres

desk verdict Sound SST-based transmission-matrix retrieval with real experiments and released code; the 'broadband' claim rests on emulated sources and the phase-locking assumption needs a direct check. read the letter →

arxiv 2607.29047 v1 pith:H7VCACXJ submitted 2026-07-31 physics.optics

Marcos Maestre Morote , Mickael Mounaix , Andrew Komonen , Martin Plöschner , Joel Carpenter This is my paper · ORCID
classification physics.optics
keywords transmissionmatrixmultimodefibrespatialstatetomographyself-referencingbroadbandlightbeamshapingintensity-onlymeasurementphaselocking
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the full complex transmission matrix of a multimode fibre can be recovered from intensity-only camera recordings, with no external reference arm, no preselected internal reference, and no iterative phase retrieval. The method uses spatial state tomography: it launches a complete set of pairwise mode-interference patterns into the fibre, records the intensities on a camera, and at each pixel reconstructs the input modal superposition that focuses light there. Missing phases between pixels are stitched together by exploiting the fact that when the camera resolves each speckle grain with several pixels, neighbouring focusing solutions must be in phase. The authors demonstrate this on a 420-mode fibre with coherent, low-coherence, and broadband sources, and use the recovered matrix for distal beam shaping. If correct, the technique removes the main obstacle to controlling light through complex media with short-coherence or broadband sources.

What carries the argument

The central mechanism is spatial state tomography (SST), applied to each camera pixel in parallel. SST generalises Stokes polarimetry: the mode space of the fibre is treated as an N-dimensional Hilbert space, and a complete set of analyser states—the eigenvectors of the Gell–Mann matrices, realised experimentally as pairwise mode interferences at four phase offsets plus single-mode launches—is used to measure a high-dimensional Stokes vector at every pixel. Multiplying the measured intensities by a sparse weighting matrix K reconstructs the pixel's density matrix; its leading eigenvector is the focusing solution for that output position. The second ingredient is the phase-locking rule: when

What would settle it

Run SST on the same fibre while deliberately coarsening the camera pixels until the speckle grain is sampled by fewer than four pixels (M²<4N); if beam-shaping overlap against the target field stays high, the in-phase condition is not load-bearing, and if it collapses, the condition is confirmed as the critical resource. A second check: on a short acquisition to avoid drift, compare the SST matrix with an off-axis holography matrix; any systematic phase error concentrated in particular mode groups would identify where the assumption fails.

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Extended reading notes

Core claim

Stated in the paper's terms: the transmission matrix of a complex medium can be measured without any phase reference by turning the measurement into a high-dimensional Stokes-polarimetry problem at every output pixel. For each of the 2N²−N analyser states launched at the input, the camera records an intensity; at each pixel the stack of intensities is converted, through the Gell–Mann operator basis, into an N×N density matrix. Its dominant eigenstate is the input field that maximises power delivery to that pixel. Because the camera oversamples the speckle grain by at least four pixels, adjacent pixels' focusing solutions must share a phase, so the per-pixel phase offsets can be recovered and

Load-bearing premise

The result stands or falls on the smoothness condition—taken from earlier work rather than re-derived here—that when the camera samples each speckle grain with at least four pixels (M²≥4N), the input fields needed to focus on neighbouring camera pixels are in phase; if that fails for any mode group, or drift breaks the phase relation during the long sequential acquisition, the cross-pixel stitching and the final matrix are corrupted.

Editorial extensions

If this is right

  • Point-scanning fibre imaging requires only the per-pixel eigenstates, so the phase-locking stage can be skipped when the goal is focusing or scanning rather than a full complex matrix.
  • For a broadband source, the matrix measured with that source's own bandwidth outperforms the monochromatic matrix for shaping light over that bandwidth; for full-mode targets the best matrix extends the usable bandwidth by about √2 relative to the monochromatic one.
  • The measurement does not need a camera array: a scanned single photodiode, a spectrometer, or a nonlinear detector could carry the same self-referencing idea into spectrally resolved or time-gated regimes.
  • Exploiting the known mode-group structure of graded-index fibre reduces the number of input projections from O(N²) to a sum over mode groups, making per-wavelength acquisition time practical with faster modulators.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The core resource is spatial oversampling of the speckle pattern, not anything specific to optical fibres; the same per-pixel tomography plus phase stitching should transfer to any linear scattering medium whose output speckle can be resolved, such as tissue or multimode waveguides.
  • Because the phase reference is distributed across all modes, the method's failure mode is not reference blindness but stability: the sequential 2N²−N projections assume the medium is static over the whole acquisition, so fast-moving media would need faster projection hardware or sparse recovery.
  • Secondary eigenstates, which the paper treats mostly as noise or residual decorrelation, may be a practical resource: they carry information about modes that decorrelate from the main solution, so a target-dependent combination of the per-eigenstate matrices could improve broadband shaping beyond the dominant-eigenstate matrix.
  • The paper's suggested connection to the broadband flux matrix A=∫S(λ)t†(λ)t(λ)dλ points to a quantitative definition of a 'source-matched transmission matrix' that future work could test by comparing SST against spectrally resolved holography followed by spectral weighting.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes an automatic self-referencing technique, spatial state tomography (SST), to measure the full complex transmission matrix (TM) of a multimode fibre from intensity-only camera frames. The method launches 2N^2−N analyser states based on Gell–Mann matrices, reconstructs a density matrix at each output pixel, and recovers the relative phase between pixels by exploiting the assumption that neighbouring pixels within one speckle grain share the same focusing input state up to a global phase. The authors demonstrate the approach on a 420-mode OM1 graded-index fibre under long-coherence (1300 nm) illumination and under emulated short-coherence/broadband sources obtained by summing monochromatic swept-source frames. They benchmark the recovered TM against off-axis digital holography and demonstrate distal beam shaping for several target fields. Data and processing code are made publicly available.

Significance. If the method is sound, it offers a deterministic, source-matched TM measurement that avoids external references, iterative phase retrieval, and preselected internal references, potentially extending wavefront shaping to broadband or low-coherence sources where holographic references are difficult. The paper is supported by a large experimental dataset, reproducible code (GitHub/Zenodo), and extensive supplementary material, which are strengths. The central idea of using distributed local interference as a phase reference is novel and well-motivated. However, the validity of the phase-locking step and the extent to which the broadband claim is supported by emulated measurements need careful scrutiny. The claims are plausible but not yet fully established by the evidence presented.

major comments (4)
  1. [Methods A, Eqs. (2)–(3)] The phase-locking step assumes that input states required to focus on neighbouring pixels within one speckle grain are identical up to a global phase. The manuscript justifies this only by citing [5, 21] and does not provide any direct validation, such as the distribution of |⟨φ′_ref|φ_target⟩| for adjacent pixels, nor a sensitivity analysis to the speckle oversampling factor M²≥4N. If the inner products in Eq. (2) have magnitude below 1, the arg operation averages distinct vectors and propagates phase errors across the camera plane. Since every downstream beam-shaping result inherits this stitching step, the authors should validate the assumption explicitly, ideally with a drift-free full-mode comparison against DH.
  2. [Results, 'Short coherence source experimental results'; Methods D, Eq. (5)] The 'broadband' and 'low-coherence' demonstrations are not measurements with a true broadband source: they are emulated by summing monochromatic swept-source intensity frames (Methods D, Eq. 5). The title and abstract claim 'broadband control' and operation 'across coherent, low-coherence, and broadband regimes' without this qualification. While the emulation is physically meaningful under static conditions, the authors should clearly state that the source bandwidth is implemented in post-processing and that the method has not been demonstrated with an actual short-coherence source. Additionally, the 'source-matched optimal' claim is not benchmarked against an independent gold standard; the link to the flux matrix in [44] is only a hypothesis.
  3. [Fig. 2 and Supplementary Note 3] The LCS benchmark is ambiguous. In Fig. 2 the complex overlap of MTM_SST is worse than MTM_DH for most patterns; the authors attribute this to reference-arm aberrations and mechanical drift (Supplementary Note 3) and then switch to an intensity-overlap metric that favours their method. The attribution to drift is asserted rather than demonstrated. A fair comparison requires a drift-controlled or interleaved measurement of both matrices under the same time window, and a report of the complex overlap distribution. Without this, the claim that SST performs 'at the level of off-axis digital holography' is not yet supported.
  4. [Supplementary Note 0, 'Non-ideal tomography'] The paper relies on the assertion that noise and drift 'predominantly corrupt the eigenvalues... while the eigenvectors remain robust' to justify recovering the primary eigenstate from imperfect measurements. This is load-bearing because the phase-locking step uses these eigenvectors, not the eigenvalues. No empirical or simulated evidence is given for this stability. The authors should provide a quantitative analysis, e.g., by comparing eigenvector overlap between repeated measurements or by injecting simulated drift into the raw data and showing that the recovered phase offsets remain stable.
minor comments (4)
  1. [Global] The text contains several typos and placeholder remnants: 'T omographic' (Supplementary Note 0), 'F or' (Abstract), 'demostrated' (Discussion), 'untagle' and 'constitude' (Supplementary Note 1). The supplementary video link is shown as 'YouTube link' rather than an actual URL. These should be cleaned up.
  2. [Fig. 2 and Supplementary Note 3] The labels in Fig. 2 refer to 'Referenceless Digital holography' while the text also uses 'MTM_DH'; please unify terminology. The intensity-overlap figure (S8) should be referenced in the main text where complex overlap results are discussed, otherwise the switch of metrics can be confusing.
  3. [Methods A / Discussion] The condition M²≥4N is cited from [5,21] but not derived for the SST pipeline. Since the phase-locking algorithm is central, a brief explanation or reference to the exact proof would improve the self-containedness of the paper.
  4. [Discussion] The authors state that the method could be extended to spectrally resolved TM or time-gated measurements, but these are speculative. It would be helpful to mark such extensions clearly as future work, not as demonstrated capabilities.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TM recovery is a genuine measurement benchmarked against digital holography; the phase-locking smoothness assumption is a physical prior, not a reduction to its own inputs.

full rationale

The derivation chain is self-contained and not circular. Per-pixel density-matrix recovery (Supplementary Eq. S3) uses tomographic projections onto Gell–Mann analyser states; the dominant eigenstate is, by the spectral theorem, the input superposition that maximizes power to that pixel. This is a definitional property of the density matrix, not a fitted prediction. The cross-pixel phase-locking (Methods A, Eqs. 2–3) relies on an explicit physical smoothness assumption: 'if the pixels on the camera are at least four times smaller than the diffraction-limited spot size (speckle grain) of the supported fibre modes (M² ≥4N), the input states necessary to focus on neighbouring pixels on the camera must be in phase.' That is a modeling prior, asserted rather than derived in this paper and cited to prior work [5,21]. It is not an equation that reduces to the measured intensities; it is an independently testable assumption. The paper does validate the full pipeline against off-axis digital holography and through beam-shaping overlap integrals, so the central result does not depend solely on the self-citation. The broadband 'source-matched optimal' claim—that the dominant eigenstate φ₁ of the source-averaged density matrix 'optimises the light control for that particular source'—is true by construction, since φ₁ maximises the source-averaged transmitted power. However, the paper does not present this optimality as a derived prediction; it states it as a property of the eigenstate and then demonstrates it experimentally via beam shaping. The only self-citation (Plöschner et al. [5], a co-author of this work) appears for the oversampling condition, but that condition is corroborated by the independent reference [21] and by the external DH benchmark. No equation in the paper is equivalent to its own inputs by construction, and the assumptions are explicit and not hidden under a fitted parameter. Thus, there is no significant circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim introduces no new physical entities and uses no fitted constants in the TM reconstruction. The main load-bearing premises are standard quantum-tomography mathematics, the physical smoothness of the transmission matrix across speckle grains, and the equivalence between emulated and real broadband illumination. None of these are circular, but the first two are not independently verified in this paper.

free parameters (2)
  • Gell-Mann analyser-state uniqueness threshold Θ = 1 - 1/N² (N = 420)
    Supplementary Note 0: a new eigenstate is retained as an analyser state only if ⟨Ω_k|Ω_r_j⟩ < Θ. This is a hand-chosen numerical threshold, not fitted to data, but it determines which input states are used.
  • Sub-noise eigenvalue threshold = not specified
    Supplementary Note 0: 'threshold sub-noise eigenvalues before extracting the eigenstates'. The threshold value is not quantified; the authors argue the principal eigenvector is robust to it, but its exact value is not reported.
assumptions (6)
  • standard math Standard density-matrix tomography formalism: Gell-Mann matrices, Born rule, spectral theorem, Eq. (S1)-(S8).
    Supplementary Note 0. The reconstruction of per-pixel density matrices from intensity projections rests on this formalism.
  • domain assumption The multimode fibre is a linear, time-invariant, wavelength-dependent system fully described by a transmission matrix.
    Introduction and Methods E; all TM retrieval methods assume this.
  • domain assumption The SLM accurately generates the required analyser states in the LG mode basis with sufficient fidelity.
    Supplementary Note 2: proximal alignment and Zernike aberration correction are described; the fidelity of every analyser-state hologram is assumed adequate.
  • domain assumption Neighbouring camera pixels within the same speckle grain have focusing solutions that are in phase when M² ≥ 4N.
    Main text phase-locking paragraph and Methods A, Eq. (2)-(3). This is the key premise for cross-pixel phase recovery; it is cited from refs [5,21], not derived here.
  • domain assumption Summing monochromatic intensity frames over a wavelength range faithfully emulates a short-coherence source.
    Methods D, Eq. (5): I_ΔλS(x,y,k) = Σ I(x,y,k)_i. This requires mutual incoherence of spectral components and Nyquist sampling δν ≤ Λ/2; it is stated but not experimentally validated against a real broadband source.
  • ad hoc to paper The observed complex-overlap deficit for MTM_SST is caused by reference-arm aberrations and mechanical drift, not by SST error.
    LCS results section: the paper explains the DH-favouring complex OI by the external reference wave and long acquisition drift. This is a post-hoc explanation without a direct control experiment.

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Cite this review

Pith. "Pith review of Broadband Control of Light through Complex Media via Automatic Self-Referencing Transmission Matrix Characterisation." pith.science (2026). https://pith.science/paper/H7VCACXJ

@misc{pith2026260729047,
  author       = {Pith},
  title        = {Pith review of: Broadband Control of Light through Complex Media via Automatic Self-Referencing Transmission Matrix Characterisation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H7VCACXJ}},
  note         = {Machine review of arXiv:2607.29047}
}
abstract

Light propagation through complex media underpins critical optical technologies, from imaging distant stars and ground-to-space communication to imaging inside biological tissue with hair-thin multimode fibre endoscopes. Central to controlling light through such disordered media lies the transmission matrix. Inaccessible to accurate modelling, the transmission matrix must be measured experimentally$-$yet this conventionally relies on techniques involving an external phase reference. For low-coherence or broadband sources, the stringent coherence, mode-matching, temporal-overlap, and stability requirements of that external reference can make such characterisation prohibitively difficult or fundamentally infeasible. Alternatively, existing self-referencing techniques use algorithmically fragile global optimisation methods, relying on fixed preselected internal reference(s), whose incomplete overlap with the transmitted field can create measurement blind spots. Here, we introduce an automatic self-referencing measurement technique based on spatial state tomography that circumvents these coherence and algorithmic limitations. Rather than relying on a preselected reference or complex phase retrieval, our approach systematically leverages the local interference among all propagating modes as distributed phase references without prior assumptions. We demonstrate this framework experimentally for a multimode fibre across coherent, low-coherence, and broadband regimes, recovering its complete optical transmission matrix and performing high-fidelity spatial and polarisation beam shaping in each case. By enabling robust, source-matched, self-referencing transmission-matrix measurement, our method extends light control through complex media into broadband illumination regimes relevant to biomedical imaging, optical communications, and high-power laser applications.

Figures

Figures reproduced from arXiv: 2607.29047 by the authors.

Figure 1
Figure 1. Optical setup, SST and phase locking working principle. (a) Optical setup composed of three color-coded stages. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) Experimental (a.1) MTM [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Mode transmission matrix analysis for different low coherent sources. Measured MTM [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Study of the performance of each measured MTM [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Iterative phase-locking logic. A master reference [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.